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This article is cited in 2 scientific papers (total in 2 papers)
Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
G. Feldera, L. J. Stevensb, A. N. Varchenkob a Departement für Mathematik, Eidgenösische Technische Hochschule
Zürich
b Department of Mathematics, University of North Carolina at Chapel Hill
Abstract:
We consider the space of elliptic hypergeometric functions of the $\mathfrak{sl}_2$ type associated with elliptic curves with one marked point. This space represents conformal blocks in the $\mathfrak{sl}_2$ WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the $\mathfrak{sl}_2$ type.
Key words and phrases:
Elliptic hypergeometric functions, conformal blocks, Macdonald polynomials.
Received: October 2, 2002
Citation:
G. Felder, L. J. Stevens, A. N. Varchenko, “Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator”, Mosc. Math. J., 3:2 (2003), 457–473
Linking options:
https://www.mathnet.ru/eng/mmj95 https://www.mathnet.ru/eng/mmj/v3/i2/p457
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Abstract page: | 285 | References: | 59 |
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